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lecture notes-Chapter5-posted

# lecture notes-Chapter5-posted - Chapter 5 Circular Motion...

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1 Chapter 5: Circular Motion Uniform Circular Motion Radial Acceleration Banked and Unbanked Curves Circular Orbits Nonuniform Circular Motion Tangential and Angular Acceleration Artificial Gravity

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3 Examples of circular motion Wheels of cars Propellers on airplanes Hard disks ……………….

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4 § 5.1 Uniform Circular Motion Here, v 0. The direction of v is changing. If v 0, then a 0. The net force cannot be zero. Consider an object moving in a circular path of radius r at constant speed. x y v v v v
5 Conclusion: to move in a circular path, an object must have a nonzero net force acting on it.

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7 θ is the angular position. Angular displacement: i f θ θ θ - = Note: angles measured CW are negative and angles measured CCW are positive. θ is measured in radians. 2 π radians = 360 ° =1 revolution x y θ i θ f ∆θ To simplify description: angles instead of distances

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8 The average and instantaneous angular velocities are: t t t = = θ ϖ θ ϖ 0 av lim and ϖ is measured in rads/sec.
9 An object moves along a circular path of radius r; what is its average speed? av av time total distance total ϖ θ θ r t r t r v = = = = Also, ϖ r v = (instantaneous values). x y θ i θ f r ∆θ

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10 x y θ i θ f ∆θ r arclength = s = r ∆θ r s = θ ∆θ is a ratio of two lengths; it is a dimensionless ratio!
Question 1 An object is in uniform circular motion. Which of the following statements is true? A) Velocity = constant B) Speed = constant C) Acceleration = constant

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Question 2 A CD makes one complete revolution every tenth of a second. The angular velocity of point 4 is: A) the same as for pt 1. B) twice that of pt 2. C) half that of pt 2. D) 1/4 that of pt 1. E) four times that of pt 1.
13 The time it takes to go one time around a closed path is called the period (T). T r v π 2 time total distance total av = = Comparing to v=r ϖ : f T π π ϖ 2 2 = = f is called the frequency , the number of revolutions (or cycles) per second.

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16 § 5.2 Centripetal Acceleration The velocity of a particle is tangent to its path. For an object moving in uniform circular motion, the acceleration is radially inward.
17 The magnitude of the radial acceleration v r r v a r ϖ ϖ = = = 2 2

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19 Example (text problem 5.14): The rotor is an amusement park ride where people stand against the inside of a cylinder.

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lecture notes-Chapter5-posted - Chapter 5 Circular Motion...

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